Volume 65 | Issue 1 | Year 2019 | Article Id. IJMTT-V65I1P512 | DOI : https://doi.org/10.14445/22315373/IJMTT-V65I1P512
This paper aim to study some types of generalized inverse for every finite matrix A (square or rectangular ) of real or complex elements with the property that the general solution of the equation A x 0 n for all positive integer n .also study Existence and Construction of Generalized , Inverses like pseudo inverse , Moore– Penrose inverse, and Properties of {1}-Inverses Drazin inverse , another types of inverses of matrices and gives some important proofs of theories .with some examples about this subject .
[1] I.Fredholm , Sur une classe d’équations fonctionnelles. Acta thematica, 27(1), 365–390 , 1903.
[2] W.A.,Hurwitz, On the pseudo-resolvent to the kernel of an integral equation. Transactions of the American Mathematical Society, 13(4) , 1912 .
[3] E.H Moore, On the reciprocal of the general algebraic matrix , Bulletin of the American Mathematical Society, 26, 52, 1920 .
[4] F.J.,Murray & Von Neumann, J , On rings of operators Annals of Mathematics, Second Series, 37(1), 116–229 , 1936.
[5] R.,Penrose, A generalized inverse for matrices., Mathematical Proceedings of the Cambridge Philosophical Society, 51, 1955.
[6] Bjerhammar, A generalized matrix algebra , Trans. Roy. Inst. , no. 124, 32 pp. , 1958 .
[7] M.P. Drazin , Pseudo inverses in associative rings and semigroups, Amer. Math. Monthly 65 , 1958 .
[8] A.G.Fisher, On Construction &, properties of the Generalized, inverses, SIAM J. , Application. Math. 15 , 1967 .
[9] N.Urquhart , Computation of generalized inverse matrices which satisfy specified conditions. SIAM Review, 10, 216–218 , 1968.
[10] S.L.Campbell , On continuity properties of the Moore – penrose and Drazin Generalized inverses , Ibid. 18, 53-57 , 1977 .
[11] J.D..,Fulton , Generalized inverses of matrices over a finite field., Discrete Mathematics, 21(1), 23–29 , 1978.
[12] J.D..keckic , on some generalized inverses of matrices and some linear matrix equations , Nouvelle serie tome 45(59) , 1989 .
[13] Y.Wel & G. wang , The parturbtion theory for the drazin inverse and its applications", shanghat Normal University,China , Elsevier , 1997.
[14] Wu, C. K., & Dawson, E. (1998b). Generalized inverses in public key crypto system key crypto system design , IEE-Proceedings-Computers and Digital Techniques, 145(1), 1998 .
[15] A.,Ben-Israel, .& . T. , Greville,. Generalized inverses: Theory and applications., 2nd edn. , Springer Verlag , New York , CMS Books in Mathematics , Rutgers University , 2003 .
[16] S.L.,Campbell, & Meyer, C. D. , Generalized , inverses of linear transformations. Classics in Applied Mathematics. Philadelphia: Society for Industrial and Applied Mathematics, 2009 .
[17] H.Hudzikand & Yu. Wang , Construction of some Generalized Inverses of Operators between Banach Spaces and their Selections, Perturbations and Applications , By Haifeng Ma Presented to the Faculty of Mathematics and Computer Science , Adam Mickiewicz University , 2011.
[18] GÜ.Meltem , (2016) , Generalized Inverses of Matrices and Applications to coding Theory, A Thesis Submitted to the Dokuz EYliil University , İZMİR. .
[19] G.R.Wang , Yimin Wei &, S.Z.Qiao, Generalized Inverses: Theory and Computations , Graduate Text book of Shanghae science press , Springer , 2018 . https://www.researchgate.net/publication/240015816_Generalized_Inverses_Theory_and_Computations
[20] Michael Friendly , (2018) , Generalized , inverse , http://www.cran.proiect.org/ web/packages/maltb , 2018.
[21] J.Uhlmann , A Generalized Matrix Inverse that is Consistent with Respect to Diagonal Transformations , SIAM J. Matrix Analysis, Vol. 239, No. 2, IJMTT Journal , 2018.
Muntaha Khudair Abbas, "Properties on Some Types of Generalized Inverses of Matrices-A Review," International Journal of Mathematics Trends and Technology (IJMTT), vol. 65, no. 1, pp. 66-72, 2019. Crossref, https://doi.org/10.14445/22315373/IJMTT-V65I1P512